Man of Honour
Come on, now you're pushing the bounds of believability!
Indeed, let's not be naive here. Anyway, stop worrying.
There is nothing in UK law stopping you scannign the letter and putting it on here. I would bet a small amount of money that within a few minutes it's be obvious to either be a scam or a law firm scare mongering.
As for the £700 for an out of court settlement, I wouldn't pay a penny of it. Even in the very unlikely circumstances that you were sued for this, the damages awarded would probably be less that this anyway, assuming it was just one illegal download. You must remember, the UK doesn't have punative damages, only compensatory.
So, my advice, post the letter here for us to have a look at, if it's not an obvious scam, see a solicitor and get them to draft a letter asking for proof of the allegations.
Burnsy